Analytical Model of Surge Flow in Nonprismatic Permeable Channels and Its Application in Arid Regions

A surge running down a dry wadi bed as a consequence of a controlled water release from a reservoir—e.g., for artificial groundwater recharge—represents a free boundary problem. After some time, when aiming for groundwater recharge, the infiltration equals inflow and thus forms a kind of “standing” wave. The numerical solution of such phenomena generally involves considerable problems. For avoiding the numerical inconvenience resulting from the complex interacting surface/subsurface flow, we present an analytical solution of the slightly modified zero-inertia (ZI) equations. The development introduces a momentum-representative cross section for portraying the transient development of momentum and refers to a channel with constant slope, irregular geometry, and a permeable channel bed with significant infiltration. Due to the structure of the solution, any arbitrary infiltration model can be used for quantifying the infiltration losses. For both synthetic prismatic and nonprismatic test channels, the robust and easy-to-use analytical ZI model shows an excellent match with the results of a comparative numerical simulation. Finally, the ZI model is employed for simulating a surge flow downstream of the Wadi Ahin groundwater recharge dam (Oman), in order to perform a scenario for artificial groundwater recharge in a natural wadi channel reach. This realistic application illustrates the potential of the new approach by even computing an almost standing wave and shows its applicability for an accurate and robust evaluation of release strategies.